How to capture variable inside lambda

As mch said in the comment, the problem is that k is not a compile time constant.

For a compile time constant, to iterate from N to 0, you may need template and recursion:

#include <algorithm>
#include <tuple>
#include <type_traits>
#include <vector>

using namespace std; // just for simplify, and not recommended in practice

template <size_t N, typename Iterator, enable_if_t<N == 0, int> = 0>
void foo(Iterator begin, Iterator end)
{
    sort(begin, end,
        [](const auto &t1, const auto &t2) {
            return get<0>(t1) < get<0>(t2); 
        }
    );
}

template <size_t N, typename Iterator, enable_if_t<N != 0, int> = 0>
void foo(Iterator begin, Iterator end)
{
    sort(begin, end,
        [](const auto &t1, const auto &t2) {
            return get<N>(t1) < get<N>(t2); 
        }
    );
    foo<N - 1>(begin, end);
}

int main()
{
    vector<tuple<int, int>> v{{0, 1}, {0, 0}, {1, 1}};
    foo<1>(v.begin(), v.end());

    // posible results:
    // {0, 0}, {0, 1}, {1, 1}
    // {0, 1}, {0, 0}, {1, 1} // impossible if use std::stable_sort instead
}

std::get only accepts a template argument which is an expression whose value that can be evaluated at compiling time. You can't use k, because it is a variable that changes value.

std::sort(begin(v), end(v), [](auto const &t1, auto const &t2) {
    const int k = 3;
    return std::get<k>(t1) < std::get<k>(t2); // or use a custom compare function
});

As I wrote in the comments, I know const int = 3 will shadow the k value outside of the lambda expression, but this example shows that get will work when it it receives a compiling time constant value. For example, if you try to set k = 5, for example where v only has 4 tuple parameters, the compiler will give an error because it knows that this is out of range.

The following code will give an error, but if k is set to 3, it will work

std::vector<std::tuple<int, int, int, int>> v;
std::sort(begin(v), end(v), [](auto const &t1, auto const &t2) {
            const int k = 5;
            return std::get<k>(t1) < std::get<k>(t2); // or use a custom compare function
        });